First debuted alongside iOS 5, Find My Friends lets you know where your friends and family are at any given time, either perpetually or for a specifically delimited time. The app's new update builds upon this theme, leveraging location geofencing so that you not only can find out where your friends are--but when they leave or arrive at a certain place.
The new feature, Notify Me, lets you set up an alert for when your friend arrives or leaves a certain address. You can get to it by tapping on an individual contact and tapping the Notify Me button; from there, choose whether you want the alert to fire when they enter or exit, and at what address. This is surprisingly useful for timing meetups with friends: If you're walking distance from a restaurant and your other friends are driving, you can set a geofence at a stoplight several blocks away; when they go through it, you'll get a notification and can start walking. (Also helpful, I've found, for timing carpool rides to work.) This feature only works on contacts who have upgraded their app to the latest version of Find My Friends and are running iOS 5 or later.
You can also flip this feature around and notify others of your location--either currently, or when you leave or arrive somewhere. Unlike Notify Me, you can send these notifications to anyone--whether they have Find My Friends installed or not. If your contact isn't using Find My Friends, they'll receive an email with your current location (or when you left or arrived); if they are, they'll get an alert from the app.
These notifications can also be set up as repeating alerts; if you want your significant other to know when you leave work, for instance, you can set up a notification to ping them every time you do. (There's no specification beyond Repeat Every Time, unfortunately, so you can't set it up at time intervals.)